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.TH LGAMMA 3M "Jul 12, 2006" "SunOS 5.11" "Mathematical Library Functions"
.SH NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, gamma, gammaf,
gammal, gamma_r, gammaf_r, gammal_r \- log gamma function
.SH SYNOPSIS
.LP
.nf
c99 [ \fIflag\fR... ] \fIfile\fR... \fB-lm\fR [ \fIlibrary\fR... ]
#include <math.h>

extern int signgam;

\fBdouble\fR \fBlgamma\fR(\fBdouble\fR \fIx\fR);
.fi

.LP
.nf
\fBfloat\fR \fBlgammaf\fR(\fBfloat\fR \fIx\fR);
.fi

.LP
.nf
\fBlong double\fR \fBlgammal\fR(\fBlong double\fR \fIx\fR);
.fi

.LP
.nf
\fBdouble\fR \fBgamma\fR(\fBdouble\fR \fIx\fR);
.fi

.LP
.nf
\fBfloat\fR \fBgammaf\fR(\fBfloat\fR \fIx\fR);
.fi

.LP
.nf
\fBlong double\fR \fBgammal\fR(\fBlong double\fR \fIx\fR);
.fi

.LP
.nf
\fBdouble\fR \fBlgamma_r\fR(\fBdouble\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.LP
.nf
\fBfloat\fR \fBlgammaf_r\fR(\fBfloat\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.LP
.nf
\fBlong double\fR \fBlgammal_r\fR(\fBlong double\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.LP
.nf
\fBdouble\fR \fBgamma_r\fR(\fBdouble\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.LP
.nf
\fBfloat\fR \fBgammaf_r\fR(\fBfloat\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.LP
.nf
\fBlong double\fR \fBgammal_r\fR(\fBlong double\fR \fIx\fR, \fBint *\fR\fIsigngamp\fR);
.fi

.SH DESCRIPTION
.sp
.LP
These functions return
.sp
ln||~(x)|
.sp
.LP
where
.sp
|~(x) = integral from 0 to +Infinity of pow(t,x-1)*exp(-t) dt
.sp
.LP
for x > 0 and
.sp
|~(x) = n/(|~(1-x)sin(nx))
.sp
.LP
for x < 1.
.sp
.LP
These functions use the external integer \fBsigngam\fR to return the sign of
\fB|~(x)\fR while \fBlgamma_r()\fR and \fBgamma_r()\fR use the user-allocated
space addressed by \fBsigngamp\fR.
.SH RETURN VALUES
.sp
.LP
Upon successful completion, these functions return the logarithmic gamma of
\fIx\fR.
.sp
.LP
If \fIx\fR is a non-positive integer, a pole error occurs and these functions
return +\fBHUGE_VAL\fR, +\fBHUGE_VALF\fR, and +\fBHUGE_VALL\fR, respectively.
.sp
.LP
If \fIx\fR is NaN, a NaN is returned.
.sp
.LP
If \fIx\fR is 1 or 2, +0 shall be returned.
.sp
.LP
If \fIx\fR is \(+-Inf, +Inf is returned.
.SH ERRORS
.sp
.LP
These functions will fail if:
.sp
.ne 2
.mk
.na
\fBPole Error\fR
.ad
.RS 14n
.rt
The \fIx\fR argument is a negative integer or 0.
.sp
If the integer expression (\fBmath_errhandling\fR & \fBMATH_ERREXCEPT\fR) is
non-zero, then the divide-by-zero floating-point exception is raised.
.RE

.SH USAGE
.sp
.LP
An application wanting to check for exceptions should call
\fBfeclearexcept\fR(\fBFE_ALL_EXCEPT\fR) before calling these functions. On
return, if \fBfetestexcept\fR(\fBFE_INVALID\fR | \fBFE_DIVBYZERO\fR |
\fBFE_OVERFLOW\fR | \fBFE_UNDERFLOW\fR) is non-zero, an exception has been
raised. An application should either examine the return value or check the
floating point exception flags to detect exceptions.
.sp
.LP
In the case of \fBlgamma()\fR, do not use the expression
\fBsigngam*exp(lgamma(x))\fR to compute
.sp
`g  := |~(x)'
.sp
.LP
Instead compute \fBlgamma()\fR first:
.sp
.LP
\fBlg = lgamma(x); g = signgam*exp(lg);\fR
.sp
.LP
only after \fBlgamma()\fR has returned can \fBsigngam\fR be correct. Note that
\fB|~(x)\fR must overflow when \fIx\fR is large enough, underflow when
\(mi\fIx\fR is large enough, and generate a division by 0 exception at the
singularities \fIx\fR a nonpositive integer.
.SH ATTRIBUTES
.sp
.LP
See \fBattributes\fR(7) for descriptions of the following attributes:
.sp

.sp
.TS
tab(	) box;
cw(2.75i) |cw(2.75i)
lw(2.75i) |lw(2.75i)
.
ATTRIBUTE TYPE	ATTRIBUTE VALUE
_
Interface Stability	See below.
_
MT-Level	See below.
.TE

.sp
.LP
The \fBlgamma()\fR, \fBlgammaf()\fR, \fBlgammal()\fR, and \fBgamma()\fR
functions are Standard. The \fBlgamma_r()\fR, \fBlgammaf_r()\fR,
\fBlgammal_r()\fR, \fBgamma_r()\fR, \fBgammaf_r()\fR, and \fBgammal_r()\fR,
functions are Stable.
.sp
.LP
The \fBlgamma()\fR, \fBlgammaf()\fR, \fBlgammal()\fR, \fBgamma()\fR,
\fBgammaf()\fR, and \fBgammal()\fR functions are Unsafe in multithreaded
applications. The \fBlgamma_r()\fR, \fBlgammaf_r()\fR, \fBlgammal_r()\fR,
\fBgamma_r()\fR, \fBgammaf_r()\fR, and \fBgammal_r()\fR functions are MT-Safe
and should be used instead.
.SH SEE ALSO
.sp
.LP
.BR math.h (3HEAD),
.BR exp (3M),
.BR feclearexcept (3M),
.BR fetestexcept (3M),
.BR isnan (3M),
.BR attributes (7),
.BR standards (7)
.SH NOTES
.sp
.LP
When compiling multithreaded applications, the \fB_REENTRANT\fR flag must be
defined on the compile line.  This flag should only be used in multithreaded
applications.
